Purchase of residential flat

Recently i was looking to buy a residential property in Mumbai and came across the following - 1. The flat is in the name of single individual (Father) since 1964. 2 However in 1998 as the father was not in good health, Father and Son gave a letter to the building society to add Sons name and Mothers name to the Share Certificate citing health reasons. 3.No gift deed was made or registered and no Stamp duty has been paid on such transfer/ addition. 4. In 2011, Mother passed away and only two names are on Share Certificate (Father & Son) 5. Father is in good health now and I am looking to Purchase flat from him What i want to know is How can share certificate be in 2 names? Because as per the original agreement, flat belongs to Father. Is such transfer/ addition of name valid? Should there be any stamp duty on such addition? Can this be considered a clear title? And what things should I be sure of before entering in any agreement? Your reply would be much appreciated Thank You.